1. Field of Invention
This invention relates to stringed instruments. More specifically, the present invention is related to a fretted stringed instrument and a method for mapping the desired location of string contact regions along the length of a fret of a stringed instrument.
2. Description of the Related Art
Fretted stringed musical instruments typically employ equal temperament tuning, equal temperament tuning being a system of musical tuning wherein the octave is divided into a series of equal steps. For example, conventional guitars utilize a twelve-tone equal temperament system wherein the twelfth fret defines the octave. The frets are typically perpendicularly disposed along the length of the fret board, and parallel to one another. The spacing of frets along the fret board is commonly calculated in accordance with a mathematical formula referred to as the “Rule of Eighteen”. Pursuant to the “Rule of Eighteen” as originally derived the vibrating length of the string (the length of the string between the points at which the string contacts the bridge and nut of the instrument) was divided by 18, with the quotient being the distance between the point at which the string initially contacts the nut and the apex or leading edge of the first fret, thereby determining the position of the first fret relative to the nut. The vibrating length of the string between the first fret and the bridge was then divided by 18 to determine the position of the second fret, with the positions of the remaining frets being determined in like manner. Subsequently, the “Rule of Eighteen” was refined to utilize 17.817 as the denominator rather than 18 (hereinafter referred to as the “modified Rule of Eighteen”). Whereas the modified “Rule of Eighteen” has been helpful in determining fret placement, and is utilized with respect to most conventional fretted instruments utilizing equal temperament tuning, it has long been recognized that the “Rule of Eighteen” is imprecise and does not provide perfect intonation of each string at each fret location. In this regard, the “Rule of Eighteen” does not take into consideration that strings are not under constant tension when a fretted stringed instrument is being played. By depressing a string, the tension on that string is increased which translates into a change in pitch, or sharpening, of the note being produced. Moreover, the amount of the increase in tension on the string increases as the fretted position gets closer to one of the structures supporting the string, i.e. the nut or the bridge. Accordingly, the pitch deviation are greater as notes are played farther from the octave, the octave being the twelfth fret where a twelve-tone equal temperament system is utilized.
Efforts have been made over the years to lessen the intonation deviations inherent in the use of the “Rule of Eighteen” system. For example, guitars and other fretted instruments have been provided with adjustable bridges, and/or adjustable nuts, which at least allow the vibrating length of individual strings to be positioned over the frets to minimize pitch deviations. E.g. U.S. Pat. No. 5,481,956. However, whereas adjustable bridges, and/or adjustable nuts, can be used to insure proper intonation at the octave or some other selected fret location, intonation deviations at other fret locations will remain due to the changing tension on the strings at other fret locations. It has long been recognized that these deviations can be compensated for by repositioning the fret along their length at individual string location. For example, early fretted instruments utilized gut string frets that were tied around the neck of the instrument and could be moved to fine tune the accuracy of the instrument. Of course, such individual adjustment of frets was difficult and the use of gut strings for frets impractical. More recently the use of frets which are angled or curved across the fret board, as opposed to traditional straight, perpendicularly disposed frets has been proposed. U.S. patent application Ser. No. 6,069,306 discloses the repositioning of frets to compensate for intonation errors inherent in instruments utilizing fret boards constructed in accordance with the “Rule of Eighteen.” However, the resulting fret board is radically different from a traditional fret board with radically differing fingering positions for the various notes. As a result the proposed instrument is extremely difficult to play. In view of the above, it will be recognized that the prior art fails to provide a practical fretted instrument offering precise intonation at each fret position without substantially compromising the playability of the instrument.
Other patents addressing the question of improving the accuracy of intonation in a fretted instrument include U.S. Pat. Nos. 3,787,600; 5,063,818; 5,750,910; 5,760,322; 5,814,745; 6,114,618; 6,426,454; 6,433,264; 6,583,346; and 6,706,957. Further patents disclosing the construction of fretted instruments include U.S. Pat. Nos. 4,064,780; 4,982,640; 5,631,432; and 6,825,406.